History dependent quantum walk on the cycle with an unbalanced coin

摘要: Abstract Recently, a new model of quantum walk, utilizing recycled coins, was introduced; however little is yet known about its properties. In this paper, we study behavior on the cycle graph. particular, will consider time averaged distribution and how it affected by walk’s “memory parameter”—a real parameter, between zero eight, which affects coin flip operator. Despite an infinite number different parameters, our analysis provides evidence that only few produce non-uniform behavior. Our also shows initial state, size modulo four all affect walk. We prove interesting relationship memory-based walk recently proposed.